Isolated scattering number of split graphs and graph products

Fengwei Li, Qingfang Ye, Xiaoyan Zhang

Abstract


Computer or communication networks are so designed that they do not easily get disrupted under external attack. Moreover, they are easily reconstructed when they do get disrupted. These desirable properties of networks can be measured by various parameters, such as connectivity, toughness and scattering number. Among these parameters, the isolated scattering number is a comparatively better parameter to measure the vulnerability of networks. In this paper we first prove that for split graphs, this number can be computed in polynomial time. Then we determine the isolated scattering number of the Cartesian product and the Kronecker product of special graphs and special permutation graphs.


doi:10.1017/S1446181117000062

Keywords


isolated scattering number, split graph, submodular function, Kronecker product, Cartesian product.



DOI: http://dx.doi.org/10.21914/anziamj.v58i0.11019



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.